CHICAGO — With their idol turning 79 in 2020, some fans of Senator Bernie Sanders who had gathered for the second annual People’s Summit were thinking wistfully about the next progressive hero who could take the presidential baton: Senator Elizabeth Warren of Massachusetts might make a good next leader, though she at times appears too cautious.

Christine Pellegrino, a Democratic New York assemblywoman, was elected to represent a district won by President Trump. If Benjamin T. Jealous, a former president of the N.A.A.C.P., wins the campaign for governor of Maryland, he has the look.

But many of the most ardent Sanders fans remain laser-focused on him. Nelson Mandela, they noted, became president of South Africa in his 70s. And Mr. Sanders is the only candidate they trust.

“That man is like superhuman,” said Joy Manbeck, 38, of Harrisburg, Pa., who got a tattoo of a finch and the word “revolution” on her arm after a finch landed on Mr. Sanders’s lectern during a campaign speech last year. “He still plays basketball. He walks to work. I don’t care. I want him. Period. I want Bernie.”

Supporters like Ms. Manbeck could hold the key to Democratic unity as the party tries to regroup after its stunning loss to Mr. Trump deprived it of all control in Washington. If Mr. Sanders declines a run in 2020, they will have to decide if they can get behind a new progressive champion in the Democratic Party; if they will accept the eventual nominee, whoever it is; or if they will take their passions — and votes — elsewhere.

Mr. Sanders’s wife, Jane, said in an interview that he had not ruled out running again and had remained active, traveling and advocating policies that help working-class people. “Ageism is the last ‘ism’ that seems to be acceptable to people, and I never felt that it was whether somebody was too young or too old,” Ms. Sanders said. “You win some. You lose some. And you keep on going and maybe you can win the next one.”

He would, after all, be only a year older than former Vice President Joseph R. Biden Jr., who has also made noises about running. And Mr. Trump, the oldest American to assume the presidency, will himself turn 74 in 2020.

But away from the boisterous People’s Summit in Chicago this weekend, some Sanders fans conceded their worries and suggested that the senator should focus on backing younger, fresh-faced candidates to push the Democratic Party leftward.

Max Weiss, a 19-year-old sophomore at the University of Illinois at Urbana-Champaign and the communications director for the Democratic Party chapter on campus, said he hoped Mr. Sanders would not run because it would be unhealthy for the party, which badly needs new faces.

He said he gets excited thinking about Democrats on the rise around the country, like Jon Ossoff, who is running in a House special election outside Atlanta, as well as Senators Al Franken of Minnesota and Kirsten E. Gillibrand of New York, who have not yet run for president.

“Sanders has the star power right now,” Mr. Weiss said. “He could transfer that to other candidates.”

The debate about the next face of the Democratic Party has left many unsure about where to go next at a critical time when Republicans plan to make big changes to immigration policies, social safety net programs, health care coverage and criminal justice issues.

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Mr. Sanders’s most devoted supporters could hold the key to Democratic unity as the party tries to regroup after its stunning loss to President Trump.CreditJoshua Lott for The New York Times

Mr. Sanders, an independent who represents Vermont, has remained close to figures who campaigned for him, such as Representative Tulsi Gabbard of Hawaii; Nina Turner, a former Ohio state senator; and Mr. Jealous.

And while the next presidential election is years away, Mr. Sanders is urging his liberal supporters to stay engaged.

“We may have lost the election in 2016, but there is no question that we have won the battle of ideas, and we are continuing that battle — and that is, brothers and sisters, no small thing,” Mr. Sanders said Saturday to raucous cheers. “The Democratic Party must finally understand which side it is on, and that cannot be the side of Wall Street or the fossil fuel industry or the drug companies.”

For some, the emotions of 2016 remain raw. Breanna Spiteri-Phillips, 37, a cook from Jackson, Mich., began to cry as she thought about Mr. Sanders’s loss to Hillary Clinton in the Democratic primaries. Ms. Spiteri-Phillips eventually voted for the Green Party candidate, Jill Stein, in the general election.

“He is the only honest candidate that I have seen in the last 20 years,” Ms. Spiteri-Phillips said as she wiped her eyes. “I’m not concerned about his age. He’s been kicking butt for the last 70 years.”

For now, Ms. Sanders said, her husband is not thinking about 2020. She said he was making sure the Democratic Party takes up issues that affect working-class families and fights policies by Mr. Trump that would worsen economic inequality.

“I’m energized by the resilience of the message of the campaign,” Ms. Sanders said. “Our focus is we’re not going to lose any ground. We’re not going to stop.”

Ms. Warren, another well-known progressive senator who has openly challenged Mr. Trump, is a logical heir to Mr. Sanders’s movement. But a few Sanders fans remain frustrated that she did not endorse him during the primary and is seemingly more reserved than the freewheeling, scruffy Vermonter.

“Bernie is very outspoken, and she seems more cautious to the point where she’s almost like trying to in a way do what people want,” said Lauren Adamson, an 18-year-old who works at a preschool and lives in Salt Lake City.

Another person on many minds is Ms. Turner of Ohio, who became a constant presence at Mr. Sanders’s campaign events. On Sunday, she spoke to the crowd for almost 40 minutes, urging the Democratic Party to focus on both white people who felt ignored in the past and blacks and Hispanics who want to see more benefits for their loyalty to the party.

“We can see what the future looks like,” she shouted through a microphone to cheers. “It’s a future that doesn’t leave anybody behind.”

Moments later, the crowd began chanting “Run, Nina, run.”

Meanwhile, even as Mr. and Ms. Sanders say they want to focus on transforming the Democratic Party, Mr. Sanders hinted that he might have another run in him. While answering a question about how to keep going after a loss, Mr. Sanders recounted that he lost many elections before being elected mayor of Burlington, Vt., and later to Congress.

“Persistence is extremely important,” Mr. Sanders said. “Yeah, you run and you lose. So what?”

Correction:June 13, 2017

An earlier version of this article misidentified the hometown of Breanna Spiteri-Phillips. She is from Jackson, Mich., not Jackson, Miss.

A version of this article appears in print on , Section A, Page 15 of the New York edition with the headline: Bushy Silver Hair At the Pinnacle Of Progressivism. Order Reprints | Today’s Paper | Subscribe